The time-varying effective reproduction number is an important parameter for communication and policy decisions during an epidemic. In this paper, we present new statistical methods for estimating the reproduction number based on the popular model of \citet{cori2013new} which defines the effective reproduction number based on self-exciting dynamics of new infections. Such a model is conceptually simple and less susceptible to misspecifications than more complicated multi-compartment models. However, statistical inference is challenging, and the previous literature has either relied on proxy data and/or a two-step approach in which the number of infections is first estimated. In contrast, we present a coherent Bayesian method that approximates the joint posterior of daily new infections and reproduction numbers using a novel Markov chain Monte Carlo (MCMC) algorithm. Comparing our method to the state-of-the-art three-step estimation procedure of \citet{huisman2022estimation}, both using daily confirmed cases from Switzerland in the Covid-19 epidemic and simulated data, we find that our method is more accurate in terms of point estimates and uncertainty quantification, especially near the beginning and end of an observation period.

翻译：时变有效再生数是疫情期间信息通报与政策决策的重要参数。本文基于\citet{cori2013new}提出的经典模型，提出估计再生数的新统计方法。该模型以新感染病例的自激动态为基础定义有效再生数，概念简洁且不易产生复杂多室模型的设定偏差。然而其统计推断颇具挑战，现有文献或依赖代理数据，或采用先估算感染人数再行分析的两步法。与此不同，我们提出了一种连贯的贝叶斯方法，通过新型马尔可夫链蒙特卡洛（MCMC）算法逼近每日新感染病例与再生数的联合后验分布。将本方法与\citet{huisman2022estimation}提出的先进三步估计流程进行对比，两者均使用瑞士Covid-19疫情期间的每日确诊病例及模拟数据。实证表明，本方法在点估计与不确定性量化方面更为精确，尤其在观测期起始与末期表现显著。